Guys this is the ersieht was to tame a quetzal. All you need is a tapejara.
1) Whisle your Tapejara to follow you
2) Ride you Tapejara and surch for a quetzal
3) When you found a quetzal, go an the back of the Tapejara (dont forget that you have to make the follow whisle on Tapejara, otherwise the will Flyer to the ground)
4) Make the attack whisle while you are on the Tapejata's back, so your tapejara will follow the quetzal.
5) Just shoot the quetzal with tranq darts/arrow and make the passive whisle on the Tapejara when he is too close to the Quetzal.
6) Repeat that till the quetzal gets knocked out and enjoy your quetzal taming.
TIPP: They spawn near the Obelisk and fly trought the whole map after spawning. GOOD LUCK!